Wavelength bands of light or other radiation can be isolated in a system. For example, a system with a detector can be configured such that a detector receives as input only a narrow range of wavelengths, while eliminating, as input to the detector, as much light at other wavelengths as possible, where such other light can be considered “noise.” Optical components that isolate one or more bands of wavelengths are called “band-pass filters.” The width of a pass-band for conventional near-UV, visible, and near-IR optical band-pass filters can range from less than 1 nm to a few nm (or less than about 1% of the center wavelength of the pass-band) for so-called “narrowband” filters to several tens of nm (about 1 to 10% of the center wavelength) for most band-pass filters—such as those used in fluorescence detection and imaging systems. The width of some band-pass filters can be several tens of percent of the center wavelength wide.
A thin-film interference filter conventionally referred to as a “narrow-band-pass” (i.e., NBP) filter can be constructed from a series of “quarter-wave” layers of material that alternate between a high-index-of-refraction material and a low-index-of-refraction material. A “quarter-wave” layer is a thin layer of material with an optical thickness that is equal to ¼ λ (or an odd-integer multiple of ¼ λ), where λ is the wavelength associated with a center of the transmission band. (The “optical thickness” of a layer of material with an index of refraction n and a geometrical thickness t is the product n×t.) A series of quarter-wave layers can create a “stop band” that is approximately centered about the wavelength λ by which the quarter-wave layers are calibrated (where the “quarter-wave” layers can have an optical thickness of (2z+1) (¼ λ) where z can be 0, 1, 2, . . . ). The “stop band” is a region of low transmittance, which is created due to destructive interference between internally-reflected and incident light through the layers of material. An NBP filter can be constructed from a series of layers by interspersing, within a stack of quarter-wave layers, resonant “cavity” layers. A “cavity” layer in an NBP filter can be an integral multiple of half-wave layers (i.e., its optical thickness is equal to: ½ λ; 1 λ; 1½ λ; etc.) of the λ associated with the quarter-wave layers. The presence of cavity layers interspersed within quarter-wave layers (where the quarter-wave layers are responsible for a stop band) can cause a relatively narrow portion of the stop band to transmit light rather than block light. A quarter-wave stack with more than one resonant cavity is referred to as a “multi-cavity” filter. The presence of multiple cavity layers can have the effect of increasing both the steepness of the cut-on edge of a transmitting region of the stop band and the steepness of the cut-off edge of the transmitting region of the stop band.
FIG. 1 depicts the structure of a conventional multi-cavity band-pass filter 100 that can provide the functionality of a NBP filter. As depicted in FIG. 1, a half-wave cavity layer 110-1 is adjacent to a quarter-wave layer 120-1, which is adjacent to a quarter-wave layer 130-1, which is adjacent to a quarter-wave layer 120-2, etc. The reference wavelength associated with the structure in FIG. 1 is λa. In FIG. 1, the optical thickness of each quarter-wave layer is approximately ¼ λa (where in general the optical thickness can be (2z+1) (¼ λa) where z can be 0, 1, 2, . . . ), and the optical thickness of each cavity layer is approximately ½ λa (where, in general, the optical thickness can be integer multiples of approximately ½ λa). As indicated by the hash-fill in the drawing, the material of the quarter-wave layer 120-1 in the depicted example can be the same as the material of the quarter-wave layer 120-2. Furthermore, the material of the half-wave cavity layer 110-1 in the depicted example can be the same as the material of the quarter-wave layer 130-1. As indicated by the suffix “n” used in FIG. 1, a quarter-wave layer 130-n can correspond to an nth repeated quarter-wave layer adjacent to (or “below,” in the figure) the quarter-wave layer 130-1. Moreover, a quarter-wave layer 120-(n+1) can correspond to an (n+1)th repeated quarter-wave layer below the quarter-wave layers 120-1 and 120-2. An additional half-wave cavity layer 110-2 can be below the half-wave cavity layer 110-1 and the series of quarter-wave layers beginning with quarter-wave layer 120-1 and ending with the quarter-wave layer 120-(n+1). Again the material of the half-wave cavity layer 110-2 in the depicted example can be the same material as the half-wave cavity layer 110-1 and the quarter-wave layers 130-1 and 130-n. 
FIG. 2 depicts an exemplary transmission curve 211 associated with the multi-cavity band-pass filter 100 for s-polarized light over a wide range of wavelengths (graph 250-1) and over a smaller range of wavelengths associated with the transmission curve 210 in the immediate vicinity of the narrow-band-pass region (graph 250-2). Graph 250-1, depicting a wide range of wavelengths, depicts the cut-off edge 212 associated with the quarter-wave layer stop band for s-polarized light, and also depicts the cut-on edge 214 associated with the quarter-wave layer stop band for s-polarized light.
Graph 250-2 depicts the relatively narrow transmission band for s-polarized light, located approximately in the center of the stop band, and associated with the added cavity layers 110-1, 110-2, etc. The transmission curve 210 has an associated cut-on wavelength 220 for s-polarized light within the stop band and a cut-off wavelength 225 for s-polarized light within the stop band. Although the transmission curve 210 at the cut-on wavelength 220 and the cut-off wavelength 225 that is depicted in FIG. 2 (and elsewhere) is shown with a relatively steep slope, an actual “edge” at the cut-on and cut-off wavelengths can exhibit some discernible slope. Accordingly, as used herein, a cut-on wavelength associated with an edge is the wavelength that is approximately half-way between the wavelength at the approximately 10% transmission point and the wavelength at the approximately 90% transmission point as part of the rising edge of the transmission curve. Further, as used herein, a cut-off wavelength associated with an edge is the wavelength that is approximately half-way between the wavelength at the approximately 90% transmission point and the wavelength at the approximately 10% transmission point as part of the falling edge of the transmission curve.
FIGS. 3 and 4 depict a set of exemplary transmission curves 310-1, 310-2, and 310-3 in the vicinity of the narrow-pass-band region associated with the multi-cavity band-pass filter 100 for s-polarized light, where incident s-polarized light 303-1, 303-2, and 303-3 strikes the multi-cavity band-pass filter 100 at different incident angles. The multi-cavity band-pass filter 100 at a particular angle of incidence is indicated in FIG. 3 by a suffix “X” in the reference number 100-X, where: multi-cavity band-pass filter 100-1 is at normal incidence to incident s-polarized radiation 303-1; multi-cavity band-pass filter 100-2 is between normal incidence and 60 degrees angle-of-incidence to incident s-polarized radiation 303-2; and multi-cavity band-pass filter 100-3 is at approximately 60 degrees angle-of-incidence to incident s-polarized radiation 303-3.
Each transmission curve 310-X (where, as depicted, “X” can take on the values of “1,” “2,” and “3”) has an associated cut-on wavelength 420-X and a cut-off wavelength 425-X. Moreover, each depicted transmission curve 310-X has an associated full-width-half-maxima (“FWHM”) value 430-X in the narrow-pass-band region. In each graph 350-X, the regions immediately outside of the FWHM values 430-X are part of the stop band associated with the plurality of quarter-wave layers 120-x and 130-x as depicted in FIGS. 1 and 2 (where x can be 1, 2, . . . n).
Graph 350-1 in FIGS. 3 and 4 depicts an exemplary transmission curve 310-1 for s-polarized light where the incident s-polarized light 303-1 strikes the multi-cavity band-pass filter 100-1 at normal incidence. The transmission curve 310-1 depicts a cut-on wavelength 420-1 and a cut-off wavelength 425-1 and a FWHM value 430-1.
Graph 350-2 depicts an exemplary transmission curve 310-2 for s-polarized light where the incident s-polarized light 303-2 strikes the multi-cavity band-pass filter 100-2 at an angle-of-incidence 302-2 between normal incidence and approximately 60 degrees from normal incidence. The transmission curve 310-2 depicts a cut-on wavelength 420-2 and a cut-off wavelength 425-2 and a FWHM value 430-2.
Graph 350-3 depicts an exemplary transmission curve 310-3 for s-polarized light where the incident s-polarized light 303-3 strikes the multi-cavity band-pass filter 100-3 at an angle-of-incidence 303-3 at approximately 60 degrees from normal incidence. The transmission curve 310-3 depicts a cut-on wavelength 420-3 and a cut-off wavelength 425-3 and a FWHM value 430-3.
As depicted in FIGS. 3 and 4, there are at least two general features of the transmission curves 310-X for s-polarized light that can change as the angle of incidence 302-X progresses between approximately normal angle of incidence and approximately 60 degrees angle of incidence. One general feature that can change is that the FWHM value 430-X of the series of transmission curves 310-X will tend to decrease as the angle of incidence 302-X progresses from approximately normal to approximately 60 degrees from normal. Further still, both the cut-on wavelength 420-X and the cut-off wavelength 425-X will tend to shift to lower wavelengths. Accordingly, although there is a shifting of both the cut-on wavelength 420-X and the cut-off wavelength 425-X as a function of the angle of incidence 302-X, there is also a decrease in the FWHM value 430-X as a function of the angle of incidence 302-X. Both of these general features are generically depicted in FIG. 5. That is, as used herein, a “center wavelength” is the arithmetic average of the cut-on wavelength and the cut-off wavelength associated with a transmission pass-band. For example, a center wavelength of the transmission curves depicted in FIG. 4, as a function of an angle of incidence of the multi-cavity band-pass filter 100 to incident s-polarized radiation, is the arithmetic average of the cut-on wavelengths 420-X and the cut-off wavelength 425-X at each angle of incidence (which is represented by the possible values of X). Further a full-width-half-max (“FWHM”) value 430-X of the transmission curves depicted in FIG. 4 as a function of an angle of incidence of the multi-cavity band-pass filter 100 to incident s-polarized radiation is the full width of the pass-band at the half-maximum value of the absolute peak of the transmission curve 310-X in the transmission pass-band region. Curve 500-1 in FIG. 5 depicts a set of center wavelength values of s-polarized light, where the general trend of a center wavelength value as a function of increasing angle-of-incidence is to decrease; and curve 500-2 depicts a set of FWHM values of s-polarized light, where the general trend of a FWHM value as a function of increasing angle-of-incidence is also to decrease.